{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:F3553SRCIUU5SWNMZC7TO4M4BC","short_pith_number":"pith:F3553SRC","schema_version":"1.0","canonical_sha256":"2efbddca224529d959acc8bf37719c08ac0b5dd3aa7387859c9d5e226261b271","source":{"kind":"arxiv","id":"1810.07381","version":1},"attestation_state":"computed","paper":{"title":"The lambda invariants at CM points","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Hongbo Yin, Peng Yu, Tonghai Yang","submitted_at":"2018-10-17T04:27:50Z","abstract_excerpt":"In the paper, we show that $\\lambda(z_1) -\\lambda(z_2)$, $\\lambda(z_1)$ and $1-\\lambda(z_1)$ are all Borcherds products in $X(2) \\times X(2)$. We then use the big CM value formula of Bruinier, Kudla, and Yang to give explicit factorization formulas for the norms of $\\lambda(\\frac{d+\\sqrt d}2)$, $1-\\lambda(\\frac{d+\\sqrt d}2)$, and $\\lambda(\\frac{d_1+\\sqrt{d_1}}2) -\\lambda(\\frac{d_2+\\sqrt{d_2}}2)$, with the latter under the condition $(d_1, d_2)=1$. Finally, we use these results to show that $\\lambda(\\frac{d+\\sqrt d}2)$ is always an algebraic integer and can be easily used to construct units in "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1810.07381","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NT","submitted_at":"2018-10-17T04:27:50Z","cross_cats_sorted":[],"title_canon_sha256":"105930e5b937bc62480943d3647af2f5cc7df3d275f05c746569a313fb4b8056","abstract_canon_sha256":"76681cbfbfba470dc1502ad2e63cfb0c00cbdf506864af16faf1382986f35e11"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:56.571188Z","signature_b64":"Uke05LN38ryXRvO7Rzz2p3CQ4pzxdLYVdZKvcgb4GiOwGc0sNWlWi6FrhvFb0aJLmtprDDnSkrmA2OQ9Z0KZDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2efbddca224529d959acc8bf37719c08ac0b5dd3aa7387859c9d5e226261b271","last_reissued_at":"2026-05-18T00:02:56.570478Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:56.570478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The lambda invariants at CM points","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Hongbo Yin, Peng Yu, Tonghai Yang","submitted_at":"2018-10-17T04:27:50Z","abstract_excerpt":"In the paper, we show that $\\lambda(z_1) -\\lambda(z_2)$, $\\lambda(z_1)$ and $1-\\lambda(z_1)$ are all Borcherds products in $X(2) \\times X(2)$. We then use the big CM value formula of Bruinier, Kudla, and Yang to give explicit factorization formulas for the norms of $\\lambda(\\frac{d+\\sqrt d}2)$, $1-\\lambda(\\frac{d+\\sqrt d}2)$, and $\\lambda(\\frac{d_1+\\sqrt{d_1}}2) -\\lambda(\\frac{d_2+\\sqrt{d_2}}2)$, with the latter under the condition $(d_1, d_2)=1$. Finally, we use these results to show that $\\lambda(\\frac{d+\\sqrt d}2)$ is always an algebraic integer and can be easily used to construct units in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.07381","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1810.07381","created_at":"2026-05-18T00:02:56.570588+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.07381v1","created_at":"2026-05-18T00:02:56.570588+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.07381","created_at":"2026-05-18T00:02:56.570588+00:00"},{"alias_kind":"pith_short_12","alias_value":"F3553SRCIUU5","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_16","alias_value":"F3553SRCIUU5SWNM","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_8","alias_value":"F3553SRC","created_at":"2026-05-18T12:32:22.470017+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/F3553SRCIUU5SWNMZC7TO4M4BC","json":"https://pith.science/pith/F3553SRCIUU5SWNMZC7TO4M4BC.json","graph_json":"https://pith.science/api/pith-number/F3553SRCIUU5SWNMZC7TO4M4BC/graph.json","events_json":"https://pith.science/api/pith-number/F3553SRCIUU5SWNMZC7TO4M4BC/events.json","paper":"https://pith.science/paper/F3553SRC"},"agent_actions":{"view_html":"https://pith.science/pith/F3553SRCIUU5SWNMZC7TO4M4BC","download_json":"https://pith.science/pith/F3553SRCIUU5SWNMZC7TO4M4BC.json","view_paper":"https://pith.science/paper/F3553SRC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.07381&json=true","fetch_graph":"https://pith.science/api/pith-number/F3553SRCIUU5SWNMZC7TO4M4BC/graph.json","fetch_events":"https://pith.science/api/pith-number/F3553SRCIUU5SWNMZC7TO4M4BC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F3553SRCIUU5SWNMZC7TO4M4BC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F3553SRCIUU5SWNMZC7TO4M4BC/action/storage_attestation","attest_author":"https://pith.science/pith/F3553SRCIUU5SWNMZC7TO4M4BC/action/author_attestation","sign_citation":"https://pith.science/pith/F3553SRCIUU5SWNMZC7TO4M4BC/action/citation_signature","submit_replication":"https://pith.science/pith/F3553SRCIUU5SWNMZC7TO4M4BC/action/replication_record"}},"created_at":"2026-05-18T00:02:56.570588+00:00","updated_at":"2026-05-18T00:02:56.570588+00:00"}